Contents

# p?gbtrf

Computes the
LU
factorization of a general n-by-n banded distributed matrix.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?gbtrf
function
computes the
LU
factorization of a general
n
-by-
n
real/complex banded distributed matrix
A
(1:
n
,
ja
:
ja
+
n
-1) using partial pivoting with row interchanges.
The resulting factorization is not the same factorization as returned from the LAPACK
function
?gbtrf
. Additional permutations are performed on the matrix for the sake of parallelism.
The factorization has the form
A
(1:
n
,
ja
:
ja
+
n
-1) =
P
*
L
*
U
*
Q
where
P
and
Q
are permutation matrices, and
L
and
U
are banded lower and upper triangular matrices, respectively. The matrix
Q
represents reordering of columns for the sake of parallelism, while
P
represents reordering of rows for numerical stability using classic partial pivoting.
Product and Performance Information
Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.
Notice revision #20201201
Input Parameters
n
(global) The number of rows and columns in the distributed submatrix
A
(1:
n
,
ja
:
ja
+
n
-1);
n
0
.
bwl
(global) The number of sub-diagonals within the band of
A
( 0 ≤
bwl
n-1
)
.
bwu
(global) The number of super-diagonals within the band of
A
( 0 ≤
bwu
n-1
)
.
a
(local)
Pointer into the local memory to an array of local size
lld_a
*
LOCc
(
ja
+
n
-1)
where
lld_a
2*
bwl
+ 2*
bwu +1
.
Contains the local pieces of the
n
-by-
n
distributed banded matrix
A
(1:
n
,
ja
:
ja
+
n
-1) to be factored.
ja
(global) The index in the global matrix
A
indicating the start of the matrix to be operated on (which may be either all of
A
or a submatrix of
A
).
desca
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
A
.
If
dtype_a
= 501
, then
dlen_
7
;
else if
dtype_a
= 1
, then
dlen_
9
.
laf
(local) The size of the array
af
.
Must be
laf
(
nb_a
+
bwu
)*(
bwl
+
bwu
)+6*(
bwl
+
bwu
)*(
bwl
+2
*bwu
)
.
If
laf
is not large enough, an error code will be returned and the minimum acceptable size will be returned in
af
[0]
.
work
(local) Same type as
a
. Workspace array of size
lwork
.
lwork
(local or global) The size of the
work
array
(
lwork
1)
. If
lwork
is too small, the minimal acceptable size will be returned in
work
[0]
and an error code is returned.
Output Parameters
a
On exit, this array contains details of the factorization. Note that additional permutations are performed on the matrix, so that the factors returned are different from those returned by
LAPACK
.
ipiv
(local) array.
The size of
ipiv
must be
nb_a
.
Contains pivot indices for local factorizations. Note that you
should not alter
the contents of this array between factorization and solve.
af
(local)
Array of size
laf
.
Auxiliary fill-in space. The fill-in space is created in a call to the factorization
function
p?gbtrf
and is stored in
af
.
Note that if a linear system is to be solved using
p?gbtrs
after the factorization
function
,
af
must not be altered after the factorization.
work
[0]
On exit,
work
[0]
contains the minimum value of
lwork
required.
info
(global)
If
info
=0
, the execution is successful.
info
< 0
:
If the
i
-th argument is an array and the
j-
th entry
, indexed
j
- 1,
info
= -(
i
*100+
j
); if the
i-
th argument is a scalar and had an illegal value, then
info
=
-i
.
info
>
0
:
If
info
=
k
NPROCS
, the submatrix stored on processor
info
and factored locally was not nonsingular, and the factorization was not completed.
If
info
=
k
>
NPROCS
, the submatrix stored on processor
info
-
NPROCS
representing interactions with other processors was not nonsingular, and the factorization was not completed.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.